arXiv:1002.2592 · Journal of Physics A Mathematical and Theoretical

Classical statistical mechanics approach to multipartite entanglement

Paolo Facchi A, Giuseppe Florio, Ugo Marzolino, Giorgio Parisi A, Saverio Pascazio

Published May 12, 2010• 33 citations

Abstract

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.

DOI: 10.1088/1751-8113/43/22/225303

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arXiv:1002.2592 · Journal of Physics A Mathematical and Theoretical

Classical statistical mechanics approach to multipartite entanglement

Paolo Facchi A, Giuseppe Florio, Ugo Marzolino, Giorgio Parisi A, Saverio Pascazio

Published May 12, 2010• 33 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8113/43/22/225303

Related papers

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Abstract We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally multipartite entangled states. They have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. We investigate their structure and consider several examples for small n. Key words Entanglement, quantum nonlocality, quantum information, Hilbert spaces 1Abstract We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally multipartite entangled states. They have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible bipartitions. We investigate their structure and consider several examples for small n. Key words Entanglement, quantum nonlocality, quantum information, Hilbert spaces 1

Jan 1, 200814 citations

We investigate multipartite entanglement in a particular family of pure

n

-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of

2^n

classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes (

n \leq 5

), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems (

n = 6

and

7

), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.